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avatar+18 

Problem: If \(log{}_{2}x=7\),find \(log{}_{8}x.\)

 

I am not allowed to use a calculator on this problem. 

These are steps I have so far:

27=x

 

x=128

 

log8128=y

 

8y=128

 

y=\(\frac{log 128}{log 8}\)

And this is where I am stuck. I have to use a calculator for this part. Is there a way to solve this without using a calculator?

Thanks.

 Jun 19, 2021
 #1
avatar+524 
+3

So far, you're doing really well..

After \(y = {log128\over log8}\)  you don't really need a calculator to solve this 

 

We can write this as

   \(y= {log 2^7\over log 2^3}\)  right?

then \(y= {7log2\over 3log2}\)

     ⇒\(y={7\over 3}\)

      

     \({log}_{8}x = {7\over 3}\)

 

 

Hope you got it :)

 Jun 19, 2021
edited by amygdaleon305  Jun 19, 2021
 #2
avatar+18 
+2

Oh yea you can write it like that then use the log rules and division. Thanks for the help!

LightningSidd  Jun 19, 2021

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